The Age of the Unthinkable (7 page)

Scientists call systems like the sandpile or the universe “nonlinear,” precisely because their internal dynamics routinely
disrupt the idea that you can expect a given action to produce the same reaction every time. If you could find a way to model
these systems, you might gain some insight into how and why they evolved over really long periods of time — exactly the sorts
of problems, puzzles of the “where did we come from and where are we going?” variety, that had stumped even the most advanced
theories. But no one had mastered the ability to model them with any accuracy, even though they were so central to science
that physicist and mathematician Stanislaw Ulam once observed that calling any part of science “nonlinear science” was like
calling any part of zoology “non-elephant zoology.” Most aspects of the world, Bak insisted, and maybe the most important
parts of the universe, were defined by being poised out of balance, moving not in a smooth line but in fits and starts. Geology
provided the easiest analogy for such thinking: southern California, after all, looks very stable most days.

The idea of a sandpile and its avalanches began as a “thought experiment” of the sort that scientists, particularly big-idea
scientists like Bak, loved: you did the math in your mind or on a computer, playing with the variables as much as you wanted
without ever having to actually step into a lab. Glenn Held, however, was an experimental scientist, so when he read what
Bak and others had written, he asked himself, “Well, what would happen if we tried this in real life?” How often
would
those sand avalanches occur? Were the ideas in Bak’s head also true in the lab? Bak had first suggested the idea in a theoretical
journal; he didn’t seem to have much of an intention to test it in reality. Could it be done? How do you build a sandpile
grain by grain? No one had ever attempted it. So Glenn Held decided to give it a try.

To begin with, Held needed grains that were more or less the same size, since clumps of sand would distort the evenness of
the pile. In pursuit of something reliably sandlike, he began experimenting with grains of aluminum oxide, but he eventually
discovered that beach sand, collected on weekend trips to the shore, was more than sandlike enough. Held filtered what he
collected to get grains of more or less the same size. He made sure that the grains were all dry (any moisture would have
altered their weight and interfered with the experiment). Then he placed the sand in a jerry-rigged machine that looked sort
of like an automatic pepper mill connected to (of course) an IBM PC. The computer controlled how fast the mill turned and
how many grains trickled out on each rotation. This allowed Held to drop the grains precisely onto a palm-sized plate. He
put the plate on a scale so he could measure how much sand was falling on and off the pile (each grain weighed .0006 ounce)
and then propped the scale inside a Plexiglas case so stray air-conditioning breezes wouldn’t disturb his pile. Building the
device took him about ten hours. Then Held turned it on.

The first sandpile, which took a day to build, the grains dropping carefully one at a time, was about two inches across on
the bottom. Just as Bak had predicted, during an initial period the pile shaped itself into a cone, an example of what physicists
call “self-organization.” No one was telling the grains where to go; the intrinsic physics of falling sand just meant that,
over time, they sorted themselves into a nice even pile instead of spraying all over the place.

Once a pile reached a certain size, Held saw, it entered that strange “critical” state Bak had anticipated. Sometimes one
additional grain would cause an avalanche; other times Held could add thousands of grains before the sand started sliding
off. Held discovered a surface pattern to the avalanches, something scientists call a “power law,” which also applies to the
distribution of other nonlinear natural phenomena, such as earthquakes. (Charles F. Richter, the father of the Richter scale,
teased the pattern from centuries of earthquake data: large earthquakes occur exponentially less frequently than small ones.
This is called a “power-law distribution.”)

But the most interesting thing about the sandpile was its fundamental unpredictability. You couldn’t take your eyes off it
for an instant. The power law told you the general chances of getting an avalanche, but would that next grain of sand set
one off? Traditional science saw the sandpile as stable, in an equilibrium state, something that might have an avalanche when
disturbed by some strong outside force or when the number of grains reached a particular quantity. But Held’s sandpile behaved
quite differently. There was no magic number. One additional grain of sand was as likely to start an avalanche as a dozen.
What happened
within
the pile, the shifting and sliding of the grains, was as important as what happened
to
the pile. There was no explicit link between how you hit the pile and how it responded, no “proportionality” between cause
and effect. Just as Bak had theorized, the sandpile was a system that could “break down not only under the force of a mighty
blow, but also at the drop of a pin.”

Held wondered how you might model such a system. Frankly, this was a difficult puzzle. Every grain on the pile was, in a sense,
linked by invisible webs of pressure and tension to every other grain. So the full dynamics of sand physics grew in complexity
a millionfold every second. New grain of sand? Okay, you had to remap
everything.
No computer could work that fast. The nature of this expanding complexity demolished the concept of prediction. “As one attempts
to make predictions further and further into the future,” Bak had speculated, “the amount of information one needs to gather
about the initial conditions increases exponentially.” And this is exactly what Held saw inside that Plexiglas case. While
you might be able to predict how one or two or even a hundred grains would interact, by the time you got to a thousand grains,
it was impossible to measure every little detail you’d need to even try to guess what was going to happen next. Such a world
was beyond the scope of even the most complex forms of Newtonian physics. In Bak’s mind there was almost no limit to how far
you might extend this logic. Any complex system likely expressed the same dynamics: the earth’s crust, ecosystems, stock markets,
international politics. Past a certain point, the internal dynamics of these systems were simply, bewilderingly unknowable.

Held tried making piles on larger and larger plates and found that, after a certain size, even the power-law distribution
of avalanches disappeared. The systems became so complex that no rules offered even a general sense of how often a grain of
sand would lead to catastrophe. You just had to sit there and watch, grain by grain, and wait. And while you sat there, you
could think about this: nothing in the history of physics or mathematics could tell you what was going to happen next.

Bak’s world wasn’t stable or well ordered. The chaos, the random, hectic shifting and shuffling of Held’s microscopic beach
particles, was an expression of energy of a sort, energy just as likely to create as to destroy. The sandpile was in a continuous
state of change; it never stood still long enough for any one set of equations to describe it fully. If Bak was right about
his theory, it should be as true outside the lab as inside — and that would demand nothing less than a complete revolution
in how the scientists around him thought. There was something profound and amazing in the dynamics of the piles, he thought:
their ability not only to translate order into chaos, but also to translate chaos into order. Sand grains, stocks, pieces
of the earth’s crust — these moved not according to some simple input and output formula but rather because of a complex logic,
where dense internal forces were as important as any outside forces. Avalanches and earthquakes expressed that logic, but
what got Bak excited was that the same physics was also at work when the sandpiles produced California from pebbles, or great
fortunes from the movement of markets. The sandpile seemed to
make
things, maybe even most of the world.

Bak liked to pass along a quote from the nineteenth-century French novelist Victor Hugo as a prescient summary of the idea:
“How do we know that the creations of worlds are not determined by falling grains of sand?” What if the real world was like
this, precariously unbalanced between stability and chaos? Bak wondered. If the logic of such a complex system could be penetrated,
even a little bit, there might be no limit to what you could create. The world wasn’t a slew of senseless randomness; it just
required new and different ways of calculating. If you could manage to discover those new ways, even the most difficult problems
would open up. This had happened before — repeatedly — in science. But if the system remained opaque? If the logic stayed
buried in those shifting sand grains? Well, then, science would continue chasing the phantoms that had undone every model
for the universe ever created. The logic of the world, even while expressing an immense inner order, would continue to appear
to us as a senseless riot.

One morning in July 2007, the investor Bill Browder woke up in his vacation house in the south of France. It was Browder’s
habit to write a letter to investors in his $2 billion Hermitage Fund once a month, not only updating them about the state
of the fund and its investments but also expressing his thoughts about the markets more generally. Browder had started doing
this more than a decade before, when he was launching Hermitage with a small investment from Edmond Safra, the legendary Lebanese
banker. Hermitage was a fund that invested in one of the most unstable markets in the world — Russia — and Browder’s ups and
downs there had made him a legend in the world of investing. (A legend not a little burnished by the fact that he was the
grandson of Earl Browder, a former head of the American Communist Party.) Browder’s investment model at Hermitage wasn’t just
to buy and sell Russian stocks. It was to buy shares in the most corrupt, worst-run Russian companies and then press them
to change. A company whose shares traded at $1 because it was overseen and looted by goons could be worth $10 a share if it
was managed even slightly better. Buy, agitate, sell: this was Browder’s strategy. And, given the people he was dealing with,
between “agitate” and “sell” he made sure he had plenty of security if need be.

Working in Russia over the years had accustomed Browder to the fact that markets could snap in ways that are largely unimaginable,
susceptible to sandpile-type forces that are invisible until they strike. In 1998, for instance, Hermitage had almost been
wiped out when the Russian stock market lost 93 percent of its value in a matter of weeks. Was this avalanche triggered by
some terrible Russian problem? Some deep hole in his investing strategy? No, the root cause was a confidence crisis that had
begun more than a year earlier. In Thailand.

Browder had been through a number of such neck-snapping “how did
that
happen” crises, and they had sharpened how he thought about markets. “When you’ve been in a market that really can go to
zero, it changes the way you think afterward,” he told me. “The main lesson is that just because something is too terrible
to contemplate doesn’t mean it’s not going to happen.” At heart Browder was someone who believed that markets could be well
run and efficient. After all, the whole premise of Hermitage was that if you could clean up companies, they could attain their
real value on the Russian exchanges. But the lesson of his years in Russia was that as solid as the foundations of a market
might look at any given moment, they were, in fact, made of sand. And if you forgot that for even an instant, you would end
up like the dozens of his fellow investors Browder had seen broken and bankrupted over his decade and a half in Russia.

In that summer of 2007, Browder was in the midst of a very good quarter — his fund was up some 30 percent in the past few
months — but this habit of living on his toes, of looking for any sign that the landscape around him was about to avalanche
away, drew his attention to a news item in the papers that July morning. In New York an auction of debt from leveraged-buyout
deals had failed to draw enough bidders and was shut down. To most of the investing world this looked simply like a small
hiccup in an otherwise well-functioning financial system. But Browder recognized it for what it was: a sign that the world
had run out of the ability to absorb new debt. It was the end of a Ponzi-like scheme and, he knew, the start of an avalanche
that might reach a historic, tragic scale. Having been through this before, in Russia, he knew exactly how bad the markets
could get. It gave him a very clear sense of what was perhaps about to happen to global markets. No preparation could be too
much. “This is it,” he told me a few days later, as we were catching up by phone. “This is the end. And it will now all start
to unravel.”

Writing to his investors that week, Browder explained that he had seen what a $40 billion hole in the Russian balance sheet
had done to that country (demolished its financial system) and that from where he sat, “a US$300-billion problem is simply
a lot larger than a US$40-billion problem, and the implications for world markets will be similarly greater.” And, he cautioned,
the final price tag on what would come to be known as the subprime-mortgage crisis was likely to be much bigger than $300
billion. Almost immediately, he began stockpiling cash, reducing his exposure to stocks as much as he could, and moving his
and his investors’ money into any safe haven he could find. He began to pioneer what he called an “off-the-grid” investing
style. “The analogy is an electrical black-out,” he wrote his investors. “Those working in an office building get paralyzed,
but those living in a cabin in the mountains hardly notice. We want to achieve the financial markets’ equivalent of living
in a cabin in the mountains.” Or, if you wanted to put it another way, he was trying to outrun a tsunami.